Need help with cracked ceiling

Hey guys, first post, and need a little help with a ceiling repair. My roof got blow off in a wind storm and I had rain leak in for about 12 hours before I could get up on the roof to patch it. Now the ceiling in my living room is damaged. The drywall is cracked and sags down an inch or 2. It's 1/2 inch drywall with a joint compound design in it but I'm not sure how to match the texture, or if its even possible to do so. So maybe someone here with experience can recognize it or has some ideas.

2. If I can't match it, what would be the next best way to fix the ceiling. I was think about cutting out the sagging area, replacing the drywall and applying a new texture like popcorn ceiling to the entire ceiling. But do you think it would cover the existing texture or would it show through?

Drywall compound and a round stippling brush. We call it stomping or stomp texturing around here. We mix a 5 gal pail of joint compound with 1 gallon of flat white latex paint. Texture thickness can be varied depending on the look you want. Just did 2,000 sf about two weeks ago. customer wanted texture no more than 1/16". Should have taken pictures when I got it done. Came out real nice. Great workout for the shoulders too.

Drywall compound and a round stippling brush. We call it stomping or stomp texturing around here. We mix a 5 gal pail of joint compound with 1 gallon of flat white latex paint. Texture thickness can be varied depending on the look you want. Just did 2,000 sf about two weeks ago. customer wanted texture no more than 1/16". Should have taken pictures when I got it done. Came out real nice. Great workout for the shoulders too.

It is posible. I don't think a first time atrtempt at it will get it done. I have matched some over the years. Some to the point that you could not see the repair. Others, depending on the light you could see it or not see it. Like anything in life...to get good you have to do the laps.

cut down and repair the damaged section. assuming you can finish the joints where they are flat and feather into the existing ceiling, this is how you create that texture. Before putting it up on the ceiling practice on a scrap piece of sheetrock first.

all the mud in your picture was put on with a roller. you'll need to mix your new mud to a consistency that will create that same depth when rolled on your new ceiling. 3/8' roller cover is fine.
when you have the mud right and you're ready to "roll". Start rolling your mud on working your way from the old to the new. It is extremely important to do this at a good pace...dont fart around.
Roll into the new ceiling about 20" across the joint and the full length of the joint.
So what you have is your mud rolled out in a "section" large enough to texture but not to laid out so mud that the mud is drying up and becomes tacky. This is important especially at this point.
because once youre happy with what you just rolled on you'll need to grab a bucket or a step ladder and cut the edge you just created on the old to new rolling. Take a 5" taping knife and pull that edge down tight to where the lap is now in the wet mud to be textured and the edge is now feather into the old.
Take your stipple brush on a handle and stomp a random pattern onto the mud you just rolled on. When stomping work your way fro the new to the old this time. This will help load your brush up with mud so when you get to the old stomp from one side of the transition to the other. so what you're doing is eliminating all the lap marks and edges. one side to the other one side to the other pulling mud off the new and putting onto the old just enough to blend the two ceilings.
repeat rolling and stomping until you completed the whole ceiling.
technique tip, you can load your stipple brush up tapping it light into the mud bucket you're using for texture. Take a bucket lid, flip it over, and stomp it until the the amount on the brush is right....what you're doing is loading up the brush to stipple thin spots...as in the transition.

Being this was your first shot at something new, here's something to consider.
Even if you didnt get a match you have a similar texture even just by technique. As a pro I can tell you that your entire ceiling, old and new, can now be textured by a pro and will cover and look as if there was never a repair. you control the outcome by how hard you sand. and you have NOT made an irreversible mistake. You'll never be able to do it if you dont attempt it. They call this DIY